Houthi second man threatened the official Yemeni government and allied Saudi-led coalition on Thursday of "hell", if Stockholm Agreement has not been fulfilled.
"Hodeida is not easy" [to take], said Mohammed Ali al-Houthi, "either peace and Sweden pact application or hell waiting for invaders and their mercenaries."
Head of Houthi Supreme Revolutionary Committee said his group told the UN envoy for Yemen that they upheld an access to Red Sea Mills in Hodeida, but "when conditions are favorable and safe.
"We call again for obligating the other party to abide by ceasefire and not to impede Sweden deal," he added.
On Tuesday Yemeni government and Houthi rebels traded blames for targeting UN liaison officers accompanying General Patrick Cammaert as heading for the Red Sea Mills.
Government officers, along with UN officers, reporters and demining team, headed to the mills and then to confrontation lines, said government spokesman.
They came under rebel intense gunfire, Rajeh Badi added, "despite prior coordination with the UN representative and Houthi promises to cease fire and remove mines."
Houthi rebels disallowed the way to be opened, denied access by UN representative and his team to the mills and asked them to return until further notice, said Badi.
On his part, Houthi spokesman stated that one of his group's de-miners had been shot dead by government forces in the presence of the UN team while opening a road leading to the mills.
This attack "discloses barbarism of aggression and their intents and lack of seriousness in applying the Sweden pact," added Dhaifullah al-Shami, who is also the Houthi information minister.
Last Friday, two of the Red Sea Mills' silos, which store large stocks of wheat, were damaged after catching fire, with the UN attributing the accident to mortar shells.
The government-held mills contain 51 thousand metric tonnes of wheat stock enough to feed 3.7 million people for a month in a country on the brink of famine.
The WFP stated on Friday that it "urgently needs to get access" to the mills on eastern fringes of the Red Sea city of Hodeida because of battles since last September.
Yemen has been racked by an armed conflict that broke out after the Iranian-backed Houthis had ousted the internationally recognized government late in 2014.
The conflict escalated after a Saudi-led coalition intervened militarily in the country in March 2015 to reinstate the government of President Hadi, pushing the country to the world's worst humanitarian crisis, according to the UN.
Parties to the nearly 4-year war in Yemen, after 8 days of peace talks in Sweden, agreed on 13 December to cease fire in Hodeida and redeploy their forces from the port city and ports of Hodeida, Salif and Ras Isa.
But the UN-brokered Stockholm Agreement is facing many challenges and difficulties to implement on ground, leading the UN Security Council to adopt a resolution deploying a mission led by Cammaert to monitor the truce.
UN monitor mission has been deployed in Hodeida to monitor rivals' compliance with Stockholm Agreement on Hodeida ceasefire and redeployment, work with both sides on providing local security forces to guard Red City and its three ports, facilitate UN support for parties in fully applying ceasefire deal, and lead and shore up a coordination plan for redeploying forces of both coalition-backed government and Iran-backed Houthi rebels.